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Detecting Earth-Like Exoplanets Using High-Dispersion Nulling Interferometry

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Detecting Earth-Like Exoplanets Using High-Dispersion Nulling Interferometry Master Thesis Detecting Earth-like exoplanets using high-dispersion nulling interferometry Supervisors : Author : Jean-Philippe BERGER Germain Garreau Guillermo MARTIN Xavier BONFILS Confidentiality : no Year 2020/2021 Detecting Earth-like exoplanets using high-dispersion nulling interferometry Garreau Germain Acknowledgment : I truly believe that in research and for many other fields, no results can be allocated to only one person but are instead the outcome of a team work, a collaboration of individuals and a lot of discussions. That is why I would like to take this opportunity to acknowledge all the persons who participated in this project and spent time helping me or sharing their knowledge with me. Firstly I want to thank everyone from the IPAG for their hospitality even during these times of pandemic implying a lower activity. I want to thank the PhD/master students who worked with me and shared tea breaks with me. I specifically thank Guillaume for using his precious time to help me resolve some of my problems when my supervisors were not available. Moreover I want to thank my supervisors Guillermo and Xavier for all the support they offered me to make sure that I could always progress in my project. And finally I want to thank my supervisor Jean-Philippe for his unlimited support and all the time he spent helping me despite his own health. This master thesis was a wonderful opportunity to work in a field I never expected to reach as an engineering student and that I wish to pursue as far as possible. i Detecting Earth-like exoplanets using high-dispersion nulling interferometry Garreau Germain The Grenoble Institute of Planetology and Astrophysics (IPAG) is the result of the merging between the Grenoble Laboratory of Astrophysics (LAOG) and the Grenoble Laboratory of Planetology (LAP) in 2011. It is part of the French National Centre for Scientific Research (CNRS) and the Grenoble-Alpes University. The institute gather an average of 170 workers: researchers, engineers, PhD students, etc... The laboratory is famous for its contribution in many instruments on the ground such as GRAV- ITY, PIONIER or SPHERE. The institute is divided into 7 teams of research studying various fields such as stellar formation, plasmas or astrochemistry. My master thesis was part of the CHARM (Contrast High Angular Resolution spectro-iMaging) and EXOPLANETES teams. ii Detecting Earth-like exoplanets using high-dispersion nulling interferometry Garreau Germain Contents Glossary v List of Figures vi 1 Introduction 1 1.1 Context . .1 1.2 Nulling interferometry: Bracewell’s principle . .1 1.3 The high-dispersion spectroscopy . .3 1.4 Goals of this study . .4 2 Simulation of the detected signal 5 2.1 Objectives . .5 2.2 The emitted signal . .5 2.3 The shot noise . .6 2.4 Implementation of a noise . .6 2.5 The background signal . .6 2.5.1 Definition . .6 2.5.2 The thermal emission . .7 2.5.3 The local zodiacal emission . .8 2.5.4 The Exozodiacal Emission . .9 2.5.5 Support for the results . .9 2.6 The interferometer limitations . .9 2.6.1 Limitations for the star light attenuation . .9 2.6.2 The stellar leakage . 10 2.7 The detector noise . 10 2.7.1 Definition . 10 2.7.2 The readout noise . 11 2.7.3 The dark current . 11 2.7.4 Example of detector noise . 11 2.7.5 Quantum efficiency . 11 3 Extracting the exoplanet signal 12 3.1 The cross-correlation function . 12 3.2 The Doppler shift of the spectra . 12 3.3 Correction of the correlation peak . 13 3.4 The high-pass filter . 15 3.5 Signal-to-noise ratio of the correlation peak . 15 4 Performance simulation 16 4.1 Design of the instrument . 16 4.2 Conditions of the simulation . 17 4.2.1 Object . 17 4.2.2 Instrument . 17 4.2.3 Software . 19 4.3 Results of the simulation . 20 iii Detecting Earth-like exoplanets using high-dispersion nulling interferometry Garreau Germain 4.3.1 Without stellar leakage . 20 4.3.2 Comments . 23 4.3.3 With stellar leakage . 23 4.4 Conclusion . 24 5 Study of a photonic device for the nulling 25 5.1 Introduction . 25 5.2 Component description . 25 5.3 Experimental setup . 26 5.4 Interferogram in the monochromatic case . 27 5.5 The contrast . 28 5.5.1 The chromatism . 29 5.5.2 The photometric equilibrium . 31 5.5.3 The relative phase instability . 31 5.6 Comments . 32 6 Conclusion 33 Appendices 36 Abstract 39 iv Detecting Earth-like exoplanets using high-dispersion nulling interferometry Garreau Germain Glossary • Astronomical Unit (A.U) : 1A.U ' 1,5.1011m • Electromagnetic wavelength: λ • ELT: Extremely Large Telescope • ESA: European Space Agency • ESO: European Southern Observatory • Jansky (Jy) : 1Jy = 10−26 W/m2/Hz • JWST: James Webb Space Telescope • LIFE: Large Interferometer For Exoplanets • Light speed: c=3.108m/s • NASA: National Aeronautics and Space Administration • NIR/MIR: Near-Infrared/Mid-Infrared • Parsec (pc) : 1pc ' 3.1016m • SNR: Signal-to-Noise Ratio • Spectral bands: – J-band: λ ∈[1.143-1.375]µm – H-band: λ ∈[1.413-1.808]µm – K-band: λ ∈[1.996-2.382]µm – L-band: λ ∈[3.42-4.12]µm – M-band: λ ∈[4.6-5.0]µm – N-band: λ ∈[7.5-14.5]µm λ • Spectral resolution: R = ∆λ • SPHERE: Spectro-Polarimetric High-contrast Exoplanet REsearch 8 • Sun radius: R ' 7.10 m • TPF-I: Terrestrial Planet Finder-Interferometer • VLT: Very Large Telescope v Detecting Earth-like exoplanets using high-dispersion nulling interferometry Garreau Germain List of Figures 1 Coronagraphic image of AB Pictoris showing a companion (bottom left). The data was obtained using a 1.4 arcsec occulting mask on top of AB Pictoris. Source: ESO......................................1 2 A schematic cartoon showing the key functional elements of a simple 2-element interferometer. Light from the two collectors travels along the optical paths d1 and d2 and is interfered and detected at the “beam combiner” in the centre of the figure. Source: [1]. .2 3 Schematic example of an interferometer output without π-phase shift for a star and an off-centered exoplanet. .3 4 Same as Fig.3 but with a π-phase shift in one of the interferometer arms. .............................................3 5 Example of light diffraction with a grating. The diffracted signal is sent to the detector in order to obtain the photon spectral distribution of the signal. .3 6 Example of differences between the star spectrum and the addition of the star and exoplanet spectrum. .4 7 Schema of the simulated situation without detailing the software part. .5 8 Emitted spectra of the star and the exoplanet with a spectral resolution of R=103 from the PSG. .5 9 Four examples of configurations from nano- to medium-size satellites. Source: [2].7 10 Example for a setup of two telescopes with diameter 0.5m, a resolution of R=103 and an optical train temperature of Toptical=60, 100 and 150K . .7 11 Example of JWST Backgrounds Tool output. Source: JWST Backgrounds Tool.8 12 Zodiacal emission spectrum according to the results of the JWST Backgrounds Tool...........................................8 13 Simulation for an exoplanet orbiting Proxima Centauri with a set of two tele- scopes with diameter D=1m and Toptical=150K. Source: [2]. .9 14 Our simulation for an exoplanet orbiting Proxima Centauri with two telescopes of D=0.5m and Toptical=150K. .9 15 Schema of the stellar leakage phenomenon for an interferometer. Source: [3]. 10 16 Example of the instrumental noise impact on the exoplanet spectrum. 11 17 Schema of the detailed software we realized with its different parts. 12 18 Example of Doppler shift depending on the radial velocity of the host star. In our case we consider the difference of velocity between the exoplanet and the host star. Source: ESO................................ 13 19 Correlation peak with an exoplanet (blue) and without (orange). The case with- out exoplanet is a false positive. 14 20 Same as in Fig.19 but with a velocity difference ∆v=50km/s between the star and the exoplanet. 14 21 Normalized correlations in the case of Fig.20 (orange) and with the correction from (11) (blue). 14 22 Example of correlation function without high-pass filtering. The large spectral structures are overwhelming. 15 −1 23 Example of correlation function with high-pass filtering with νc=50µm . The correlation peak appears. 15 vi Detecting Earth-like exoplanets using high-dispersion nulling interferometry Garreau Germain 24 Schema of the SNR calculation protocol. 16 25 Four examples of configurations from nano- to medium-size satellites. Source: [2]. 18 26 NIRSpec NRS1 and NRS2 detector performance summaries. Source: NIRSpec Detector Performance................................. 18 27 Evolution of the SNR with the cutoff resolution (1/fc) for spectral resolution R=103 (top,left), 104 (top,right), 105 (bottom,left) and 106 (bottom,right). The study is made in the K-band with t=24hrs, 1/ρ=10−6 and the shot noise as the only source of noise. 19 28 Example of a full correlation function. 20 29 Evolution of the SNR with the spectral resolution for three sources of photo- electronic noise. We consider the star light attenuation C=1/ρ=10−6 (no stellar leakage). 21 30 Evolution of the quadratic difference between the ideal case and with one source of noise. The ideal case is added as a reference but has no meaning here. 21 31 Evolution of the SNR with the spectral resolution for different background sources. We consider the star light attenuation C=1/ρ=10−6 (no stellar leakage).
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